Find the length of 13.2 kg of copper wire of diameter 4 mm,
Question:

Find the length of 13.2 kg of copper wire of diameter 4 mm, when 1 cubic centimetre of copper weighs 8.4 g.

Solution:

Mass of copper wire = 13.2 kg = 13.2 × 1000 = 13200 g        (1 kg = 1000 g)

Volume of 8.4 g of copper wire = 1 cm3

$\therefore$ Volume of $13200 \mathrm{~g}$ (or $13.2 \mathrm{~kg}$ ) of copper wire $=\frac{13200}{8.4} \mathrm{~cm}^{3}$

Let the length of the copper wire be l cm.

Radius of the copper wire, $r=\frac{4}{2}=2 \mathrm{~mm}=0.2 \mathrm{~cm} \quad(1 \mathrm{~cm}=10 \mathrm{~mm})$

$\therefore$ Volume of the copper wire $=\pi r^{2} l=\frac{22}{7} \times(0.2)^{2} \times l \mathrm{~cm}^{3}$

$\Rightarrow \frac{22}{7} \times(0.2)^{2} \times l=\frac{13200}{8.4}$

$\Rightarrow l=\frac{13200 \times 7}{22 \times(0.2)^{2} \times 8.4}$

$\Rightarrow l=12500 \mathrm{~cm}$

$\Rightarrow l=\frac{12500}{100} \quad(1 \mathrm{~m}=100 \mathrm{~cm})$

$\Rightarrow l=125 \mathrm{~m}$

Thus, the length of the copper wire is 125 m.

 

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